Problem: A local gift shop sold bags of candy and cookies for Halloween. Bags of candy cost $$8.00$, and bags of cookies cost $$4.50$, and sales equaled $$64.50$ in total. There were $6$ more bags of cookies than candy sold. Find the number of bags of candy and cookies sold by the gift shop.
Solution: Let $x$ equal the number of bags of candy and $y$ equal the number of bags of cookies. The system of equations is then: ${8x+4.5y = 64.5}$ ${y = x+6}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${x+6}$ for $y$ in the first equation. ${8x + 4.5}{(x+6)}{= 64.5}$ Simplify and solve for $x$ $ 8x+4.5x + 27 = 64.5 $ $ 12.5x+27 = 64.5 $ $ 12.5x = 37.5 $ $ x = \dfrac{37.5}{12.5} $ ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $ {y = x+6}$ to find $y$ ${y = }{(3)}{ + 6}$ ${y = 9}$ You can also plug ${x = 3}$ into $ {8x+4.5y = 64.5}$ and get the same answer for $y$ ${8}{(3)}{ + 4.5y = 64.5}$ ${y = 9}$ $3$ bags of candy and $9$ bags of cookies were sold.